This Letter presents the analysis of a new class of diffractive optical element, the odd-symmetry phase grating, which creates wavelength- and depth-robust features in its near-field diffraction pattern.
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Machine learning for the identification of phase transitions in interacting agent-based systems: A Desai-Zwanzig example.
Phys Rev E
July 2024
Department of Chemical and Biomolecular Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA.
Deriving closed-form analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs). In this paper, we propose a data-driven framework that pinpoints phase transitions for an ABM-the Desai-Zwanzig model-in its mean-field limit, using a smaller number of variables than traditional closed-form models. To this end, we use the manifold learning algorithm Diffusion Maps to identify a parsimonious set of data-driven latent variables, and we show that they are in one-to-one correspondence with the expected theoretical order parameter of the ABM.
View Article and Find Full Text PDFTwo-dimensional multi-element phase gratings can be engineered to show an even symmetry along one direction while an odd symmetry along the other direction in terms of offset refractive indices in each unit cell. The interplay of such even and odd symmetries has been explored to tailor diffraction columns and rows on demand by making offset refractive indices to satisfy specific requirements and hence attain different types of destructive interference. The resultant tailoring effects include the directional column elimination, the grouped column elimination, and the directional column selection as well as the natural row absence, the grouped row elimination, and the central row selection.
View Article and Find Full Text PDFNonadiabatic Ultracold Quantum Reactive Scattering of Hydrogen with Vibrationally Excited HD( = 5-9).
J Phys Chem A
November 2019
Theoretical Division , Los Alamos National Laboratory , Group T-1, Mail Stop B221, Los Alamos , New Mexico 87544 , United States.
The results from electronically non-adiabatic and adiabatic quantum reactive scattering calculations are presented for the H + HD( = 5-9) → H + HD(', ') reaction at ultracold collision energies from 10 nK to 60 K. Several experimentally verifiable signatures of the geometric phase are reported in the total and vibrationally and rotationally resolved rate coefficients. Most notable is the predicted 2 orders of magnitude enhancement of the rotationally resolved ultracold rates of odd symmetry relative to those of even symmetry.
View Article and Find Full Text PDFSymmetry and the geometric phase in ultracold hydrogen-exchange reactions.
J Chem Phys
August 2017
Theoretical Division (T-1, MS B221), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Quantum reactive scattering calculations are reported for the ultracold hydrogen-exchange reaction and its non-reactive atom-exchange isotopic counterparts, proceeding from excited rotational states. It is shown that while the geometric phase (GP) does not necessarily control the reaction to all final states, one can always find final states where it does. For the isotopic counterpart reactions, these states can be used to make a measurement of the GP effect by separately measuring the even and odd symmetry contributions, which experimentally requires nuclear-spin final-state resolution.
View Article and Find Full Text PDFOdd-symmetry phase gratings produce optical nulls uniquely insensitive to wavelength and depth.
Opt Lett
June 2013
Rambus Labs, Sunnyvale, California 94089, USA.
This Letter presents the analysis of a new class of diffractive optical element, the odd-symmetry phase grating, which creates wavelength- and depth-robust features in its near-field diffraction pattern.
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